What is the fee for exiting the city limits and how many km can a taxi go outside the city?

It depends on the taxi company policy.

Both independent taxis and taxi companies receive working authorization for the cities in which they operate.

Still, you can use taxi services for going outside cities, but this has to be done by mutual agreement between you and the taxi driver.
If you do not use the same taxi cab to return in the city, the taxi driver is allowed to charge you up to 80% more that the official tariff.